"Max Keon" <maxkeon@optusnet.com.au> wrote in message
news:44b4612f$0$22359$afc38c87@news.optusnet.com.au...
The anomalous acceleration of Pioneer toward the sun is guaranteed
proof of a gravity anisotropy.

Sorry - all anomalies fully explained by for example gas leaks.

Now, thanks to Jerry, I can address that problem properly. The
existence of the anisotropy is beyond doubt. All I need do is find
it.

The gravity anisotropy appeared to be turned on when Pioneer 11 flew
by Saturn and entered a hyperbolic escape trajectory, which would
carry it rapidly away from the Sun. Why do you think it wasn't
noticed before that maneuver?

Quote:

Acceleration toward the Sun at the radius of Saturn is around
2.5957E-4 m/sec^2. If Pioneer was sent off from Saturn at 20 km/sec,
pointing directly away from the Sun, the gravity force toward the
Sun would increase to g' = ((c + v)^2 / c^2) * g
= ((3e+5 + 20) ^2 / 3e+5 ^2) * 2.5957e-4 = 2.59605e-4 m/sec^2

Now, thanks to Jerry, I can address that problem properly. The
existence of the anisotropy is beyond doubt. All I need do is find
it.

The gravity anisotropy appeared to be turned on when Pioneer 11 flew
by Saturn and entered a hyperbolic escape trajectory, which would
carry it rapidly away from the Sun. Why do you think it wasn't
noticed before that maneuver?

Mostl likely, because of the large radiation pressure of the sun
within the radius of Jupiter.

The anomalous acceleration of Pioneer toward the sun is guaranteed
proof of a gravity anisotropy.

Acceleration toward the Sun at the radius of Saturn is around
2.5957E-4 m/sec^2. If Pioneer was sent off from Saturn at 20 km/sec,
pointing directly away from the Sun, the gravity force toward the
Sun would increase to g' = ((c + v)^2 / c^2) * g
= ((3e+5 + 20) ^2 / 3e+5 ^2) * 2.5957e-4 = 2.59605e-4 m/sec^2

That seems about right to me.

The gravitational acceleration due to the
Sun is:

g = GM/r^2

where M is the mass of the Sun, so your equation in
full should be:

g' = ((c + v)^2 / c^2) * GM / r^2

During the period from Jan 1987 to Dec 1994 covered
by Figure 8 in www.arxiv.org/abs/gr-qc/0104064, the
heliocentric speed fell from 12.85km/s to 12.40km/s
so was effectively constant. However the range
increased from 40AU to 61AU so the anomalous
acceleration should have fallen to (40/61)^2 or 43% of
the initial value. It was constant to within the resolution
of the measurement.

Max Keon wrote:
The anomalous acceleration of Pioneer toward the sun is guaranteed
proof of a gravity anisotropy.

Acceleration toward the Sun at the radius of Saturn is around
2.5957E-4 m/sec^2. If Pioneer was sent off from Saturn at 20 km/sec,
pointing directly away from the Sun, the gravity force toward the
Sun would increase to g' = ((c + v)^2 / c^2) * g
= ((3e+5 + 20) ^2 / 3e+5 ^2) * 2.5957e-4 = 2.59605e-4 m/sec^2

That seems about right to me.

The gravitational acceleration due to the
Sun is:

g = GM/r^2

where M is the mass of the Sun, so your equation in
full should be:

g' = ((c + v)^2 / c^2) * GM / r^2

To me, that's a confusing way to perform a very simple task. For
this case, gravitational attraction for a relatively minute mass
such as Pioneer in the realm of planets, can be determined with just
a simple comparison. Ms/Me=gs/ge (Ms = Sun mass. Me = Earth mass.
gs and ge are Sun and Earth gravity rates for a common radius
respectively). gs=(Ms/Me)*ge . gs = (1.99e30 / 5.97e24) * .0098
= 3266 km/sec^2 at 6357 km radius from the center of Sun's mass
(if the Sun was a black hole). Which gives acceleration rates for
Saturn, Uranus and Neptune of 6.45e-8, 1.59e-8 and 6.27e-9 km/sec^2
respectively.

Please let me know if that's wrong. I stuffed it up last time.

Figure 3 from the link you provided below indicates that Pioneer 11
was accelerating very slowly away from the Sun on its initial
departure from Saturn. The angle of its trajectory would give it
only about .4 km/sec outward motion. Applying the equation
g' = ((c + v)^2 / c^2) * g to that velocity, gives an anomalous
acceleration rate of 1.7e-13 km/sec^2. When it arrived at the orbit
radius of Neptune, the apparent velocity was around 6.4 km/sec. By
the equation, the anomalous acceleration rate at that radii is
2.68e-13 km/sec^2. But while it was passing by the orbit radii of
Uranus, the apparent anisotropy was 7.9e-13 km/sec^2. The peak of
the curve is toward Saturn.

The anisotropy pointing toward Saturn, generated on its departure,
would be fairly well smothered by other effects. So too would the
Sun related anisotropy.

There's still another point to be considered. In the outer reaches
of the solar system, Pioneer's motion relative to the local universe
will generate an anisotropy, and in that peaceful realm, may well
begin to become obvious. And, that anisotropy will remain fairly
constant. In this case though, Pioneer is moving away from one
gravity source, toward another.
g' = ((c - v)^2 / c^2) * g also applies.

Quote:

During the period from Jan 1987 to Dec 1994 covered
by Figure 8 in www.arxiv.org/abs/gr-qc/0104064, the
heliocentric speed fell from 12.85km/s to 12.40km/s
so was effectively constant. However the range
increased from 40AU to 61AU so the anomalous
acceleration should have fallen to (40/61)^2 or 43% of
the initial value. It was constant to within the resolution
of the measurement.

"George Dishman" <george@briar.demon.co.uk> wrote in message
news:1152719853.472225.61150@i42g2000cwa.googlegroups.com...
Max Keon wrote:
The anomalous acceleration of Pioneer toward the sun is guaranteed
proof of a gravity anisotropy.

Acceleration toward the Sun at the radius of Saturn is around
2.5957E-4 m/sec^2. If Pioneer was sent off from Saturn at 20 km/sec,
pointing directly away from the Sun, the gravity force toward the
Sun would increase to g' = ((c + v)^2 / c^2) * g
= ((3e+5 + 20) ^2 / 3e+5 ^2) * 2.5957e-4 = 2.59605e-4 m/sec^2

That seems about right to me.

The gravitational acceleration due to the
Sun is:

g = GM/r^2

where M is the mass of the Sun, so your equation in
full should be:

g' = ((c + v)^2 / c^2) * GM / r^2

To me, that's a confusing way to perform a very simple task.

It is just the basic Netonian laws, force:

f = GMm/r^2

and acceleration:

f=ma

Put them together to get

a = GM/r^2

For your version I just included your speed term.

Quote:

For
this case, gravitational attraction for a relatively minute mass
such as Pioneer in the realm of planets, can be determined with just
a simple comparison. Ms/Me=gs/ge (Ms = Sun mass. Me = Earth mass.
gs and ge are Sun and Earth gravity rates for a common radius ..
....
Please let me know if that's wrong. I stuffed it up last time.

The part that is wrong is "common radius". The distance
of the craft from the Sun increased from 40AU to 60AU
during the main period they considered and the 50%
change produces a factor of 2.25 reduction of gravity.

Quote:

Figure 3 from the link you provided below indicates that Pioneer 11
was accelerating very slowly away from the Sun on its initial
departure from Saturn. The angle of its trajectory would give it
only about .4 km/sec outward motion.

No, the speed was around 12km/s through the period.
You can use the JPL Horizons system to get lots of
this sort of basic information:

Applying the equation
g' = ((c + v)^2 / c^2) * g to that velocity, gives an anomalous
acceleration rate of 1.7e-13 km/sec^2. When it arrived at the orbit
radius of Neptune, the apparent velocity was around 6.4 km/sec. By
the equation, the anomalous acceleration rate at that radii is
2.68e-13 km/sec^2. But while it was passing by the orbit radii of
Uranus, the apparent anisotropy was 7.9e-13 km/sec^2. The peak of
the curve is toward Saturn.

The anisotropy pointing toward Saturn, generated on its departure,
would be fairly well smothered by other effects. So too would the
Sun related anisotropy.

There's still another point to be considered. In the outer reaches
of the solar system, Pioneer's motion relative to the local universe
will generate an anisotropy, ...

No, the craft was still well within the heliopause so
the only outside effect would be interstellar dust
passing through the system, and that is at far too
low a level.

Quote:

and in that peaceful realm, may well
begin to become obvious. And, that anisotropy will remain fairly
constant.

It would also be in the same direction for both craft
while in reality the anomaly accelerates both towards
the Sun and they are on opposite sides of the Solar
System. Local interstellar or galactic influences can
generally be ruled out for that reason.

The anomalous acceleration of Pioneer toward the sun is guaranteed
proof of a gravity anisotropy.

Acceleration toward the Sun at the radius of Saturn is around
2.5957E-4 m/sec^2. If Pioneer was sent off from Saturn at 20 km/sec,
pointing directly away from the Sun, the gravity force toward the
Sun would increase to g' = ((c + v)^2 / c^2) * g
= ((3e+5 + 20) ^2 / 3e+5 ^2) * 2.5957e-4 = 2.59605e-4 m/sec^2

That seems about right to me.

The gravitational acceleration due to the
Sun is:

g = GM/r^2

where M is the mass of the Sun, so your equation in
full should be:

g' = ((c + v)^2 / c^2) * GM / r^2

To me, that's a confusing way to perform a very simple task.

It is just the basic Netonian laws, force:

f = GMm/r^2

and acceleration:

f=ma

Put them together to get

a = GM/r^2

For your version I just included your speed term.

For
this case, gravitational attraction for a relatively minute mass
such as Pioneer in the realm of planets, can be determined with just
a simple comparison. Ms/Me=gs/ge (Ms = Sun mass. Me = Earth mass.
gs and ge are Sun and Earth gravity rates for a common radius ..

...

Please let me know if that's wrong. I stuffed it up last time.

The part that is wrong is "common radius". The distance
of the craft from the Sun increased from 40AU to 60AU
during the main period they considered and the 50%
change produces a factor of 2.25 reduction of gravity.

Figure 3 from the link you provided below indicates that Pioneer 11
was accelerating very slowly away from the Sun on its initial
departure from Saturn. The angle of its trajectory would give it
only about .4 km/sec outward motion.

No, the speed was around 12km/s through the period.
You can use the JPL Horizons system to get lots of
this sort of basic information:

Applying the equation
g' = ((c + v)^2 / c^2) * g to that velocity, gives an anomalous
acceleration rate of 1.7e-13 km/sec^2. When it arrived at the orbit
radius of Neptune, the apparent velocity was around 6.4 km/sec. By
the equation, the anomalous acceleration rate at that radii is
2.68e-13 km/sec^2. But while it was passing by the orbit radii of
Uranus, the apparent anisotropy was 7.9e-13 km/sec^2. The peak of
the curve is toward Saturn.

The anisotropy pointing toward Saturn, generated on its departure,
would be fairly well smothered by other effects. So too would the
Sun related anisotropy.

There's still another point to be considered. In the outer reaches
of the solar system, Pioneer's motion relative to the local universe
will generate an anisotropy, ...

No, the craft was still well within the heliopause so
the only outside effect would be interstellar dust
passing through the system, and that is at far too
low a level.

and in that peaceful realm, may well
begin to become obvious. And, that anisotropy will remain fairly
constant.

It would also be in the same direction for both craft
while in reality the anomaly accelerates both towards
the Sun and they are on opposite sides of the Solar
System. Local interstellar or galactic influences can
generally be ruled out for that reason.

George

Interjecting a possibility of obtaining more definitive data,
the following reference provides a mission
to quantify the anomalous effect
http://arxiv.org/pdf/gr-qc/0506139
3.3. A Dedicated Mission Concept

quote
"In particular,
we emphasize a precision formation flying as a feasible
flight system concept for the proposed mission. For
this architecture, a passive sphere covered with cornercube
retroreflectors is laser-ranged from the primary craft."
Unquote

This is an excellent idea.
My fear is that 'area to mass' ratio
will not be designed into the "passive sphere"

If the "passive sphere" is designed as a bowling ball rather than a soccer ball
the anomalous effect will not be measured above the noise.

Why not have several passive objects
with an array of geometric shapes with a range of 'area to mass' ratios

Acceleration toward the Sun at the radius of Saturn is around
2.5957E-4 m/sec^2. If Pioneer was sent off from Saturn at 20 km/sec,
pointing directly away from the Sun, the gravity force toward the
Sun would increase to g' = ((c + v)^2 / c^2) * g
= ((3e+5 + 20) ^2 / 3e+5 ^2) * 2.5957e-4 = 2.59605e-4 m/sec^2

That seems about right to me.

The gravitational acceleration due to the
Sun is:

g = GM/r^2

where M is the mass of the Sun, so your equation in
full should be:

g' = ((c + v)^2 / c^2) * GM / r^2

To me, that's a confusing way to perform a very simple task.

It is just the basic Netonian laws, force:

f = GMm/r^2

and acceleration:

f=ma

Put them together to get

a = GM/r^2

I seem to only get the right answer if I convert the gravitational
constant to an "acceleration constant" of my own making,
(G' = 6.6337075e-20). Was I expected to provide an appropriate
multiplier or something? G' is close to G * 1e-9. Am I just not
understanding the values that the letters now represent?

a = G'M/r^2 results in .0098 km/sec^2 for the acceleration rate
at the Earth's surface. The rest follows from that. But mass must
be in kilograms, and distance in kilometers, otherwise it stuffs
up. So, what's the correct method?

For
this case, gravitational attraction for a relatively minute mass
such as Pioneer in the realm of planets, can be determined with just
a simple comparison. Ms/Me=gs/ge (Ms = Sun mass. Me = Earth mass.
gs and ge are Sun and Earth gravity rates for a common radius ..
...
Please let me know if that's wrong. I stuffed it up last time.

The part that is wrong is "common radius". The distance
of the craft from the Sun increased from 40AU to 60AU
during the main period they considered and the 50%
change produces a factor of 2.25 reduction of gravity.

Apparently I haven't explained that properly. The "common radius"
is common only for the purpose of setting up a base radii for the
Sun at which the acceleration rate can be determined using the
already known acceleration rate on the Earth's surface at that
same radius. Once that has been done, the rest follows, for as far
as one wishes to go.

Quote:

Figure 3 from the link you provided below indicates that Pioneer 11
was accelerating very slowly away from the Sun on its initial
departure from Saturn. The angle of its trajectory would give it
only about .4 km/sec outward motion.

No, the speed was around 12km/s through the period.
You can use the JPL Horizons system to get lots of
this sort of basic information:

According to figure 3 (linked previously), Pioneer 11 left Saturn's
orbit at an angle of about 88 degrees across the line to the Sun.
If it was traveling at 12 km/sec in that direction, it was moving
away from the Sun at .42 km/sec. That rate increased on its travels
as its path became more aligned with the Sun.

Quote:

Applying the equation
g' = ((c + v)^2 / c^2) * g to that velocity, gives an anomalous
acceleration rate of 1.7e-13 km/sec^2. When it arrived at the orbit
radius of Neptune, the apparent velocity was around 6.4 km/sec. By
the equation, the anomalous acceleration rate at that radii is
2.68e-13 km/sec^2. But while it was passing by the orbit radii of
Uranus, the apparent anisotropy was 7.9e-13 km/sec^2. The peak of
the curve is toward Saturn.

The anisotropy pointing toward Saturn, generated on its departure,
would be fairly well smothered by other effects. So too would the
Sun related anisotropy.

There's still another point to be considered. In the outer reaches
of the solar system, Pioneer's motion relative to the local universe
will generate an anisotropy, ...

No, the craft was still well within the heliopause so
the only outside effect would be interstellar dust
passing through the system, and that is at far too
low a level.

Every point in space is the focal point of the entire mass of the
universe. Its effect is naturally uniformly distributed everywhere
and wouldn't be easy to detect. But it still must have some effect
on anything in motion relative to where the local base of dimension
is set, which is determined by the Sun around here. You probably
won't like that.

Quote:

and in that peaceful realm, may well
begin to become obvious. And, that anisotropy will remain fairly
constant.

It would also be in the same direction for both craft
while in reality the anomaly accelerates both towards
the Sun and they are on opposite sides of the Solar
System. Local interstellar or galactic influences can
generally be ruled out for that reason.

Not in this case. Whatever direction Pioneer is pointing, it's
moving away from the Sun's influence and more into the realm of
the universe. It's moving away from the universe in the direction
of the Sun, where the Sun is the major influence, and toward the
universe in the direction of its travels.

Acceleration toward the Sun at the radius of Saturn is around
2.5957E-4 m/sec^2. If Pioneer was sent off from Saturn at 20 km/sec,
pointing directly away from the Sun, the gravity force toward the
Sun would increase to g' = ((c + v)^2 / c^2) * g
= ((3e+5 + 20) ^2 / 3e+5 ^2) * 2.5957e-4 = 2.59605e-4 m/sec^2

That seems about right to me.

The gravitational acceleration due to the
Sun is:

g = GM/r^2

where M is the mass of the Sun, so your equation in
full should be:

g' = ((c + v)^2 / c^2) * GM / r^2

To me, that's a confusing way to perform a very simple task.

It is just the basic Netonian laws, force:

f = GMm/r^2

and acceleration:

f=ma

Put them together to get

a = GM/r^2

I seem to only get the right answer if I convert the gravitational
constant to an "acceleration constant" of my own making,
(G' = 6.6337075e-20). Was I expected to provide an appropriate
multiplier or something? G' is close to G * 1e-9. Am I just not
understanding the values that the letters now represent?

Put "gravitational constant" into Google and you will get:

6.67300 * 10^-11 m^3 kg^-1 s^-2

Note the distance units are metres. "Mass of Sun" gives:

5.9742 * 10^24 kg

"Radius of Earth" gives:

6378.1 km or 6.3781 * 10^6 m

So g = GM/r^2

= (6.673*10^-11) * (5.9742*10^24) / (6.3781*10^6)^2

= (6.673 * 5.9742 / 6.3781^2) * 10^(-11 + 24 - 6*2)

= 0.98 * 10^1

= 9.8 m/s^2

Quote:

a = G'M/r^2 results in .0098 km/sec^2 for the acceleration rate
at the Earth's surface. The rest follows from that. But mass must
be in kilograms, and distance in kilometers, otherwise it stuffs
up. So, what's the correct method?

With the conventional units, mass is in kg and
distance in metres, not kilometres.

Yes, that was the essence of my original reply
but v doesn't change much while r chages by 50%
over the period studied hence r^2 changes by a
factor of 2.25. You cannot treat it as constant.

Quote:

For your version I just included your speed term.

For
this case, gravitational attraction for a relatively minute mass
such as Pioneer in the realm of planets, can be determined with just
a simple comparison. Ms/Me=gs/ge (Ms = Sun mass. Me = Earth mass.
gs and ge are Sun and Earth gravity rates for a common radius ..
...
Please let me know if that's wrong. I stuffed it up last time.

The part that is wrong is "common radius". The distance
of the craft from the Sun increased from 40AU to 60AU
during the main period they considered and the 50%
change produces a factor of 2.25 reduction of gravity.

Apparently I haven't explained that properly. The "common radius"
is common only for the purpose of setting up a base radii for the
Sun at which the acceleration rate can be determined using the
already known acceleration rate on the Earth's surface at that
same radius. Once that has been done, the rest follows, for as far
as one wishes to go.

That's fine but then perhaps you didn't appreciate
how much the range changed over the period they
studied.

Quote:

Figure 3 from the link you provided below indicates that Pioneer 11
was accelerating very slowly away from the Sun on its initial
departure from Saturn. The angle of its trajectory would give it
only about .4 km/sec outward motion.

No, the speed was around 12km/s through the period.
You can use the JPL Horizons system to get lots of
this sort of basic information:

According to figure 3 (linked previously), Pioneer 11 left Saturn's
orbit at an angle of about 88 degrees across the line to the Sun.
If it was traveling at 12 km/sec in that direction, it was moving
away from the Sun at .42 km/sec. That rate increased on its travels
as its path became more aligned with the Sun.

The period they were able to analyse cover 5 Jan 1987
to 1 Oct 1990 for Pioneer 11. The heliocentric range
rate was amllmost constant at about 11.7 km/s while
the speed in heliocentric coordinates (along the path
rather than radial) fell from 13.7 to 12.8 km/s.

Quote:

Applying the equation
g' = ((c + v)^2 / c^2) * g to that velocity, gives an anomalous
acceleration rate of 1.7e-13 km/sec^2. When it arrived at the orbit
radius of Neptune, the apparent velocity was around 6.4 km/sec. By
the equation, the anomalous acceleration rate at that radii is
2.68e-13 km/sec^2. But while it was passing by the orbit radii of
Uranus, the apparent anisotropy was 7.9e-13 km/sec^2. The peak of
the curve is toward Saturn.

The anisotropy pointing toward Saturn, generated on its departure,
would be fairly well smothered by other effects. So too would the
Sun related anisotropy.

There's still another point to be considered. In the outer reaches
of the solar system, Pioneer's motion relative to the local universe
will generate an anisotropy, ...

No, the craft was still well within the heliopause so
the only outside effect would be interstellar dust
passing through the system, and that is at far too
low a level.

Every point in space is the focal point of the entire mass of the
universe. Its effect is naturally uniformly distributed everywhere
and wouldn't be easy to detect. But it still must have some effect
on anything in motion relative to where the local base of dimension
is set, which is determined by the Sun around here. You probably
won't like that.

What you are describing could be seen as a sort
of static version of frame dragging but the level
would be much smaller than your equation. However,
I'm not getting into that argument, I merely
pointed out that the consequence of your equation
is an anomaly that would vary with the inverse
square of the heliocentric range and what is
observed is constant.

<snip other comment, I assumed you were describing
something else so my comments were irrelevant>

I seem to only get the right answer if I convert the gravitational
constant to an "acceleration constant" of my own making,
(G' = 6.6337075e-20). Was I expected to provide an appropriate
multiplier or something? G' is close to G * 1e-9. Am I just not
understanding the values that the letters now represent?

Put "gravitational constant" into Google and you will get:

6.67300 * 10^-11 m^3 kg^-1 s^-2

Note the distance units are metres. "Mass of Sun" gives:

Thanks for clearing that up. I shouldn't have bothered you with it.
-----
-----

Quote:

There's still another point to be considered. In the outer reaches
of the solar system, Pioneer's motion relative to the local universe
will generate an anisotropy, ...

No, the craft was still well within the heliopause so
the only outside effect would be interstellar dust
passing through the system, and that is at far too
low a level.

Every point in space is the focal point of the entire mass of the
universe. Its effect is naturally uniformly distributed everywhere
and wouldn't be easy to detect. But it still must have some effect
on anything in motion relative to where the local base of dimension
is set, which is determined by the Sun around here. You probably
won't like that.

What you are describing could be seen as a sort
of static version of frame dragging but the level
would be much smaller than your equation. However,
I'm not getting into that argument, I merely
pointed out that the consequence of your equation
is an anomaly that would vary with the inverse
square of the heliocentric range and what is
observed is constant.

It's quite irrelevant anyway because the anisotropy generated in
the forward direction would be canceled by that generated in the
trailing direction.

According to the math, the anomalous acceleration remains fairly
constant, but in reality that's not the case at all. Figure 7 in
the rather exceptional link that you previously provided,
http://www.arxiv.org/abs/gr-qc/0104064 shows a reasonably
constant curve plot for the anomalous acceleration. But it's only
constant because ***the calculation is in constant error by that
amount***.

At an easily determined location between Jupiter and Saturn, the
anisotropy generated by Pioneer11's motion away from Jupiter is
canceled by the negative anisotropy generated by its motion toward
Saturn. Any gravity anisotropy generated in those close range
interactions would be well concealed by the math error anyway, but
not so for the relationship between Pioneer and the Sun because
the error is already beginning to show.

When Pioneer leaves Saturn, the anisotropy magically begins
to appear because the math error now has almost nowhere to hide.
The error is the negative of the anisotropy and reduces at a
squaring rate per distance because that's how it was necessarily
designed so as to counteract the close range anisotropy. Now Pioneer
is pointing out into a wilderness where the only significant masses
are Uranus and Neptune. But I don't think either of those planets
were anywhere near Pioneer 10 or 11's flight paths. But beyond
Neptune, the error **really** had nowhere to hide.

This is a list of the true anomalous accelerations from 10 to 50 AU
(with no Jupiter or Saturn), if you want to believe it.

No problem at all, it is the cranks that continue
to repeat errors after having them explained that
are annoying.

Quote:

What you are describing could be seen as a sort
of static version of frame dragging but the level
would be much smaller than your equation. However,
I'm not getting into that argument, I merely
pointed out that the consequence of your equation
is an anomaly that would vary with the inverse
square of the heliocentric range and what is
observed is constant.

It's quite irrelevant anyway because the anisotropy generated in
the forward direction would be canceled by that generated in the
trailing direction.

Your figures later seem to say there is a net effect.

Quote:

According to the math, the anomalous acceleration remains fairly
constant, but in reality that's not the case at all. Figure 7 in
the rather exceptional link that you previously provided,
http://www.arxiv.org/abs/gr-qc/0104064 shows a reasonably
constant curve plot for the anomalous acceleration. But it's only
constant because ***the calculation is in constant error by that
amount***.

The calculations have been repeated independently by
Markwardt as reported in:

and he finds the same anomaly, it is highly unlikely to
be a maths error.

Quote:

At an easily determined location between Jupiter and Saturn, the
anisotropy generated by Pioneer11's motion away from Jupiter is
canceled by the negative anisotropy generated by its motion toward
Saturn.

The period studied for the Pioneers started in 1987.
If you look at figure 3 in the Anderson paper you can
see that by that time Pioneer 11 was beyond the orbit
of Uranus and Pioneer 10 was beyond the orbit of
Neptune. Your comment might apply between Uranus
and Neptune for Pioneer 11 but Pioneer 10 was on the
opposite side of the Sun so of no consequence. You
seem to grasp that below though.

Quote:

Any gravity anisotropy generated in those close range
interactions would be well concealed by the math error anyway,

I don't know where you get the idea of a "math error".

Quote:

but
not so for the relationship between Pioneer and the Sun because
the error is already beginning to show.

When Pioneer leaves Saturn, the anisotropy magically begins
to appear because the math error now has almost nowhere to hide.
The error is the negative of the anisotropy and reduces at a
squaring rate per distance because that's how it was necessarily
designed so as to counteract the close range anisotropy. Now Pioneer
is pointing out into a wilderness where the only significant masses
are Uranus and Neptune. But I don't think either of those planets
were anywhere near Pioneer 10 or 11's flight paths. But beyond
Neptune, the error **really** had nowhere to hide.

Yes, that is true, Pluto was just below the path of
Voyager 1 in 1987 while Uranus and Neptune were
a little above the path of Pioneer 10.

Quote:

This is a list of the true anomalous accelerations from 10 to 50 AU
(with no Jupiter or Saturn), if you want to believe it.

I haven't checked the numbers but that illustrates
the point I made at first, these are falling as the
inverse square of the distance while the observed
anomaly was constant.

Quote:

Paradoxes and anomalies occur in mathematics, not in nature.
It's a pitty though because we really could use some anomalous
perpetual motion to get us out of trouble (for now).

Well this anomaly occurs in reality though
whether it is the effect of a real acceleration
or just something that affects the telemetry
signal frequency is still open to some debate,
and whether it is "new physics" or something
mundane like a gas leak or thermal radiation
will be argued over for a considerable time IMO.

Every point in space is the focal point of the entire mass of the
universe. Its effect is naturally uniformly distributed everywhere
and wouldn't be easy to detect. But it still must have some effect
on anything in motion relative to where the local base of dimension
is set, which is determined by the Sun around here. You probably
won't like that.

George Dishman wrote:

Quote:

What you are describing could be seen as a sort
of static version of frame dragging but the level
would be much smaller than your equation. However,
I'm not getting into that argument, I merely
pointed out that the consequence of your equation
is an anomaly that would vary with the inverse
square of the heliocentric range and what is
observed is constant.

I wrote:
-It's quite irrelevant anyway because the anisotropy generated in
-the forward direction would be canceled by that generated in the
-trailing direction.

That is not so at all. But the effect is probably insignificant.

And I wrote:
-At an easily determined location between Jupiter and Saturn, the
-anisotropy generated by Pioneer11's motion away from Jupiter is
-canceled by the negative anisotropy generated by its motion toward
-Saturn.

Which again is false.
The point in space between Jupiter and Saturn where I assumed the
gravity anisotropies would cancel each other is offset toward Saturn
at .6462786 of the distance between them. Even though they are the
negative of each other, they add together to reinforce the total
anisotropy. One is generated by motion away from Jupiter and the
other through motion toward Saturn, regarless of how they intersect.

I wrote:
Every point in space is the focal point of the entire mass of the
universe. Its effect is naturally uniformly distributed everywhere
and wouldn't be easy to detect. But it still must have some effect
on anything in motion relative to where the local base of dimension
is set, which is determined by the Sun around here. You probably
won't like that.

George Dishman wrote:
What you are describing could be seen as a sort
of static version of frame dragging but the level
would be much smaller than your equation. However,
I'm not getting into that argument, I merely
pointed out that the consequence of your equation
is an anomaly that would vary with the inverse
square of the heliocentric range and what is
observed is constant.

I wrote:
-It's quite irrelevant anyway because the anisotropy generated in
-the forward direction would be canceled by that generated in the
-trailing direction.

That is not so at all. But the effect is probably insignificant.

And I wrote:
-At an easily determined location between Jupiter and Saturn, the
-anisotropy generated by Pioneer11's motion away from Jupiter is
-canceled by the negative anisotropy generated by its motion toward
-Saturn.

Which again is false.
The point in space between Jupiter and Saturn where I assumed the
gravity anisotropies would cancel each other is offset toward Saturn
at .6462786 of the distance between them. Even though they are the
negative of each other, they add together to reinforce the total
anisotropy. One is generated by motion away from Jupiter and the
other through motion toward Saturn, regarless of how they intersect.

Be careful Max, your equation was:

(1 + (v/c)^2) * GM/r^2

but that is just the magnitude.

Since the speed enters as v^2 and (v/c) << 1 it
always produces a small increase in the magnitude
of the force. However that is directed towards
the body so if the craft is between the planets,
their contributions would tend to cancel. However,
you really need to find the vector sum because
the craft is unlikely to be directly on the line
joining the planets so there will also be a net
force perpendicular to that line at the point of
balance.

What you really need to do is plot the sum of

(v/c)^2 * GM/r^2

for the Sun and all the planets as a function of
the distance along the trajectory from 1987
onwards and split it into a component along the
path and one normal to the path. You won't get a
constant acceleration.

As a rough estimate, the Sun dominates so the total
effect will be close to an inverse square.